If you decide to take that big step, leave the comforts of vacation rentals behind, and get a real Parisian apartment, you'll probably have to set up things like EDF and internet. I have yet to sign up for EDF so I can't give any advice on that but I can on internet and that's actually surprisingly easy.
I figured you'd need your carte and your lease but nope. Nothing. I went with Bougie (Bouygues). I was going to go with Free but there was an installation charge and I didn't want to pay it. So I checked the other wifis around me and noticed that Bougie was the only one in my proximity. I went online to check to see if my building was kitted out for it and sure enough Bougie was at my address.
I decided to do it online but if you want to actually speak to a person Jonathan at the Bougie on rue de Belleville between Jourdain and Places des Fetes is really helpful. He spent 5 years living in California so he can understand your (American) concerns. If you do it online, it's simple enough. Choose your box, and plan, and then pay the price of the equipment. I think it was like 4 screens to get through total. Have your RIB for the automatic payments screen. For me it was 50€ and 19,99€ a month for phone, internet and tv. I mean it all came together so it didn't really matter I guess that I didn't have a tv or a phone for a landline. Anyhow easy peasy lemon squeezy.